UCLA
Economics 11
–
Fall 2010
Professor Mazzocco
Problem Set 7
Because of the midterm this problem set will not be graded and you do not have to
turn it in. However, solving the following exercises is excellent practice for the
midterm.
1)
Let the production function be
assume that both factors are variable.
a)
Derive the contingent demand functions for
K
and
L
.
b)
Substitute the contingent demand functions in the total cost that you minimized in
part a) to obtain the total cost function.
c)
Find the amount of K and L necessary to produce q =100 when v=2 and w=1.
d)
Find the average and marginal cost functions.
(a) Set up Lagrangian:
FOC:
From (1) and (2), we have
vK = wL
(4)
Solving (3) and (4), we have
b) Hence,
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(c) Given q = 100, v = 2, w = 1, we have
(d)
2)
Suppose that a production function is given by q=L+K
0.5
, where v is the price of K
and w is the price of L.
a)
Find the marginal productivity of labor and capital.
b)
Find the most efficient combination of inputs for producing 347 units of output when
w=4 and v=1.
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 Fall '08
 cunningham
 Economics, Microeconomics, Economics of production, Professor Mazzocco

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